To implement an optimum modulation scheme for system requirements in an optical communication system, multi-dimensional modulation techniques have been proposed which allow a spectral efficiency to be selected with a finer granularity, in addition to conventional dual polarization quadrature amplitude modulation (QAM) techniques. A conventional dual polarization QAM maps transmission data to a constellation point independently in a two-dimensional space of each of the polarized waves. In contrast, multi-dimensional modulation maps transmission data to a constellation point in a four- or higher-dimensional space formed of two polarized waves and of multiple time slots (TSs). Thus, multi-dimensional modulation can use an increased Euclidean distance between constellation points, and thus can increase noise tolerance. Multi-dimensional modulation can also increase nonlinearity tolerance by reducing signal power variations in each TS and/or increasing the level of randomness in a polarized state (see Non-Patent Literature 1). Note that mapping over n TSs is performed such that data is mapped to constellation points in a 4n-dimensional space.
Typically, in symbol mapping in multi-dimensional modulation, parity data is added to the transmission data, which is then rearranged to form data to be modulated (hereinafter referred to simply as “modulation data”), and the modulation data is mapped to constellation points of a QAM scheme or to constellation points of a 2-ary amplitude 8-ary phase shift keying (2A8PSK) scheme. Transmission data is converted to modulation data using a circuit including a look-up table (LUT) or the like or using a dedicated symbol mapping circuit applicable only to a specific multi-dimensional modulation scheme (see Patent Literature 1).